This coterminal angle calculator converts an angle in degrees or radians into two positive co-terminal angles and two negative co-terminal angles.

Coterminal Angle Formula

The following formulas are used to calculate coterminal angles.

Positive Coterminal Angle = Angle + 360
Negative Coterminal Angle = Angle -360

To calculate the coterminal angle, add and/or subtract 360 degrees from the current angle.

The formulas above would only yield one of each co-terminal angle. In reality, there is an infinite number of co-terminal angles. The definition is simply an angle that ends at the same point as another angle on a coordinate plane. Since the coordinate circle has a total rotation of 360 degrees, adding or subtracting that to the angle yields a result, as does the coterminal angle calculator above.

To calculate a coterminal angle between 0 and 2π, in terms of pi, you must add or subtract 2π from the fractional pi value given. For example:

Find the coterminal angle of 11π/3:

Since 11π/3 > 2π, subtract 2π from the given angle. If the given angle was less negative, you would add 2π.

11π/3 - 2π/1 = 11π/3 - 6π/3 = 5π/3.

Coterminal Angle Definition

A coterminal angle is an angle that ends at the same geometric point on the coordinate plane as another angle.

Common Coterminal Angle Values

The following list outlines the coterminal angles of the most commonly calculated angles.

How to calculate a coterminal angle

Let's take a look at an example of how you might calculate the coterminal angle.

  1. Let's assume you are given an angle in radians. For this example, the angle is 2.5 radians.
  2. First, you must convert the radians to degrees. 1 radian is equal to 57.29 degrees so 2.5*57.28=114.59 degrees
  3. Last, we need to add 360 degrees to that angle to find an angle that is coterminal with the original angle, so 114.59+360 = 475.59 degrees.
  4. Check the answer using the calculator above.


What is a coterminal angle?

A coterminal angle is an angle that ends at the same location as another angle. For example, 1 degree and 361 degrees are at the same location since the total angles in a circle are 360 degrees.

What is the coterminal angle formula?

The coterminal Angle can be calculated with one of the following:
Positive Coterminal Angle = Angle + 360
Negative Coterminal Angle = Angle -360